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Beliebt Rechnen >

integral of sqrt(x)(ln(x))

Lösung

\int x (ln (x)) d x

Lösung

\frac{2}{3} x^{\frac{3}{2}} ln (x) - \frac{4}{9} x^{\frac{3}{2}} + C

Schritte zur Lösung

\int x ln (x) d x

Wende die partielle Integration an

= \frac{2}{3} x^{\frac{3}{2}} ln (x) - \int \frac{2}{3} x^{\frac{1}{2}} d x

\int \frac{2}{3} x^{\frac{1}{2}} d x = \frac{4}{9} x^{\frac{3}{2}}

= \frac{2}{3} x^{\frac{3}{2}} ln (x) - \frac{4}{9} x^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} x^{\frac{3}{2}} ln (x) - \frac{4}{9} x^{\frac{3}{2}} + C

Graph

Beliebte Beispiele

integral of (x^4-x)^2

\int (x^{4} - x)^{2} d x

integral of 2x^3+2x-3

\int 2 x^{3} + 2 x - 3 d x

integral of x^{-7/2}

\int x^{- \frac{7}{2}} d x

integral of (e^{2x})/(36+e^{2x)}

\int \frac{e ^{2 x}}{36 + e ^{2 x}} d x

integral of 1/(x^4+x^6)

\int \frac{1}{x ^{4} + x ^{6}} d x